Write the equation of a line that is parallel to the given line.
1. y =- 4x

Step-by-step explanation:

A line that is parallel will have the same slope as the reference line.  The slope-intercept form of a straight line equation is:

     y = mx + b,

where m is the slope and y is the y-intercept (the value of y when x=0),

The line y = -4x has a slope of -4 and a y-intercept of 0 (it crosses the y axis when x = 0).

That means any line with the form y = -4x + b will be parallel, since the slopes are both -4.  

All that is needed is to choose a value for b, the y-intercept, to be different than 0.  Pick any number - all resulting lines will be parallel.  I'll chose b = 2.

y = -4x + 2 is parallel to y = -4x

See attached image for these two lines, plus two more I added with different values of b.